From the moment that Alex and Maia Shibutani first performed their free dance, they knew they had struck an emotional chord that would resonate with themselves and with audiences. And every time they took their “Fix You’’ program into the spotlight, that feeling grew stronger.

Saturday, it brought them something new: their first U.S. championship. The brother and sister from Ann Arbor, Mich., brought down the house at Xcel Energy Center with a rendering of a program that has enraptured crowds all season. Skating to Coldplay’s anthem of hopeful longing, the Shibutanis scored 115.47 points for the free dance, vaulting them past defending champs Madison Chock and Evan Bates.

Chock and Bates won the short dance Friday and put on another fine performance in their free dance to Rachmaninoff’s Concerto No. 2. They were awarded 111.79 points and took the silver medal with a total of 186.93. Madison Hubbell and Zachary Donohue earned bronze with 178.81.

Alex Shibutani, 24, said the pair has drawn more emotional depth from the program with each performance. Their skate Saturday conveyed the vision they had for it all along. And yet, the siblings believe they have only brushed the surface.

“That was an absolutely incredible moment for Alex and me,’’ said Maia, 21. “To become national champions for the first time is incredible.

“We’ve really reached a new level of maturity. We’ve had a strong belief in ourselves, and that’s going to be what continues to push us forward.’’

The Shibutanis were U.S. silver medalists in 2011 and 2012, then took bronze in 2013 and 2014 before moving back up to the podium’s second spot last year.

Chock and Bates hoped to defend the title they first won last year.Over the previous 16 years, Meryl Davis and Charlie White won six consecutive titles; Tanith Belbin and Ben Agosto won five in a row; and Naomi Lang and Peter Tchernyshev captured five straight.

Chock and Bates took their defeat in stride. “We’re really happy with the way we handled this week,’’ Bates said. “This has been our best competition as far as how we skated and how we performed. We’re going to take this to fuel us and make us stronger.’’

Saturday, the Shibutanis seemed to be completely lost in their music, and the crowd came along with them. Their performance began with a feeling of melancholy. It gradually rose to an emotional climax with a dramatic lift, in which Maia orbited her brother as he spun, and ended with a long embrace between the siblings.

The audience — which was hushed through much of the performance — gave them a standing ovation, hurling bouquets of stuffed roses to the ice. When the scores were announced, their coaches leapt and rejoiced, engulfing the skaters in a group hug.

Successful brother-and-sister ice dancing teams are not common, and the Shibutanis have faced their share of skeptics. The gold medal was the ultimate validation.

“We’ve never really doubted what our potential was,” Alex said.’’